Question

You are an investor with access to €1,000,000.00 or its equivalent amount in U.S.$. You want to conduct an investment. You are provided with the following quotations from a bank: Exchange rate Interest rate Spot rate (€/$ €0.7000 = $1.00 € = 4.15% per annum F360(€/$) €0.7010 = $1.00 $ = 4.7% per annum Determine whether an arbitrage opportunity exists for a one year investment and show the following in the space provided below if the arbitrage opportunity exists: Currency to be borrowed (specify $ or €): ………………… Amount to be borrowed: ………………………… Currency to be invested in (specify $ or €): ………………… Amount to be invested: …………………………

Answer 1

This seems to be a case of covered interest arbitrage

We need to compare the interest rate differential and the cost of hedging to ascertain whether an arbitrage opportunity exists.

The spot rate is 0.7€ = 1$ or 1€ = 1.429 $

The cost of hedging can be found from the one year forward exchange rate ;€0.701=1$ or 1€ = 1.426 $, so the swap points required to buy € in the forward market would be 4260 points.

Compare that to the calculated forward rate ,based on their interest rate differential

So,

F ($/€) = S($/€)*(1+i$)/(1+i€)

so F($/€) = 1.429*1.047/1.0415 = 1.4365

1€= 1.4365 $

that means a swap point of 4365 points (for forward exchange rate interest rate parity)

Covered interest arbitrage is possible only if the cost of hedging is less than the interest rate differential, which it is

4260 points lesser than 4365 points.

Hence, an arbitrage opportunity exists

Borrow 1,000,000€ , the repayment obligation would then be 41500€ after one year

Convert € to $ at the spot rate as $ has the higher interest rate, that means we have 1,429,000$

Next, lock in a deposit at 4.7% but also simultaneously enter a forward contract at the given forward rate .

So, after one year 1,429,000 $ accumulates interest of $67163 for a total of 1,496,163 $. The forward contract will lock in an exchange rate of  1€ = 1.426 $

So after one year we receive 1,496,163/1.426 = 1049202€

Payoff the loan of 1041500€ to return a profit of (1049202-1041500)€ = 7702€

So, currency to borrow: €

Amount to borrow: 1,000,000€

Currency to invest $

Amount to invest 1,429,000$